[seqfan] Re: On the Parity of Stanley's Partition Function -- should a comment go in A097567 or elsewhere?

[Meeussen Wouter (bkarnd)]

Richard,

{0, 2, 2, 0, 2, 10, 10, 2, 10, 36, 36, 12, 36, 110, 110, 46, 112, 300, 300,
146, 310, 752, 754, 410, 788, 1770, 1780, 1052, 1880, 3958, 3992, 2522, 4256,
8480, 8580, 5726, 9222, 17528, 17790, 12426, 19260, 35122, 35754, 25960,
38958, 68486, 69922, 52492, 76620, 130374, 133478, 103152, 147002, 242910,
249346, 197662, 275844, 443898, 456790, 370352, 507350, 797054, 822116,
680030, 916362, 1408376, 1455832, 1226006, 1627880, 2452130, 2539940,
2173754, 2848148, 4211710, 4370866, 3795624, 4913636, 7143244, 7426390,
6534840, 8367430, 11973886, 12469200, 11105110, 14077510, 19852532, 20705762,
18644414, 23418370, 32579104, 34028258, 30950606, 38547672, 52951090,
55380552, 50839536, 62824878, 85283872, 89307970, 82685642}

confirms your 45 values below.

You are right:  Superseeker gives just: 
	Report on [ 2,2,0,2,10,10,2,10,36,36,12,36,110,110,46,112,300,300,146,310,752]:
	Many tests are carried out, but only potentially useful information (if any) is reported here.

I suspect Superseek doesn't check the N*(N+1)/2 differences of sequence pairs.
http://www.research.att.com/~njas/sequences/superhelp.txt doesn't suggest that.
But a person might suggest a method to obtain approximately that:
like 
	(limit this to non-decreasing abs values,
	store element 1,2,3 of each sequence, say size 200K of'm;
	sort them, 
	then check element 1,2,3 of the unknown against them,
	in sofar as all three differences are >=0,
	and for those 'potentials', lookup these differences
	in the sorted set ...)
but then smarter.

It would not prove the absence of seq(x)= seq(u)-seq(v)
but it just might point to its presence.
Think 'low hanging fruit'.

Wouter.
 
___________________________________________
Richard J. Mathar wrote:


The sequence u(n)=p(n)-t(n) = A000041(n)-A097566(n) in their equation (2.5)
  = 0,0,2,2,0,2,10,10,2,10,36,36,12,36,110,110,46,112,300,300,146,310,752,754,410,
  788,1770,1780,1052,1880,3958,3992,2522,4256,8480,8580,5726,9222,17528,17790,12426,
  19260,35122,35754,25960,38958 (offset 0) (needs to be checked!) seems not to be in the OEIS(TM).

RJM
_______________________________________________
===============================
This email is confidential and intended solely for the use of the individual to whom it is addressed. 
If you are not the intended recipient, be advised that you have received this email in error and that any use, dissemination, forwarding, printing, or copying of this email is strictly prohibited.
You are explicitly requested to notify the sender of this email that the intended recipient was not reached.